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a. Find dr for the path r(t) = g(t)i + h(t)j + k(1)k. b. Evaluate the force F along the path. c. Evaluate F• dr. 63. F = xyºi + 3x(xy³ + 2)j; r(t) = (2 cos t)i + (sin t)j, 0

a. Find dr for the path r(t) = g(t)i + h(t)j + k(1)k. b. Evaluate the force F along the path. c. Evaluate F• dr. 63. F = xyºi + 3x(xy³ + 2)j; r(t) = (2 cos t)i + (sin t)j, 0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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a. Find dr for the path r(t) = g(t)i + h(t)j + k(1)k. b. Evaluate the force F along the path. c. Evaluate F• dr. 63. F = xyºi + 3x(xy³ + 2)j; r(t) = (2 cos t)i + (sin t)j, 0 <t< 27 3 j; r(t) = (cos t)i + (sin t)j, 1 + y? 64. F 1 + x? 0 <t< T 65. F = (y + yz cos xyz)i + (x² + xz cos xryz)j + (z + xy cos xyz)k; r(t) = (2cos t)i + (3 sin t)j + k, 0 <t< 2m 66. F = 2xyi – y²j + ze*k; r(t) = –ti + Vtj + 3tk, 1<t< 4 67. F = (2y + sin x)i + (z² + (1/3)cos y)j + x*k; r(t) = (sin t)i + (cos t)j + (sin 2t)k, -7/2 < i </2 68. F = (x²y)i + rj + xyk; r(f) = (cos t)i + (sin t)j + (2 sin² t – 1)k, 0<t< 2m
Transcribed Image Text:a. Find dr for the path r(t) = g(t)i + h(t)j + k(1)k. b. Evaluate the force F along the path. c. Evaluate F• dr. 63. F = xyºi + 3x(xy³ + 2)j; r(t) = (2 cos t)i + (sin t)j, 0 <t< 27 3 j; r(t) = (cos t)i + (sin t)j, 1 + y? 64. F 1 + x? 0 <t< T 65. F = (y + yz cos xyz)i + (x² + xz cos xryz)j + (z + xy cos xyz)k; r(t) = (2cos t)i + (3 sin t)j + k, 0 <t< 2m 66. F = 2xyi – y²j + ze*k; r(t) = –ti + Vtj + 3tk, 1<t< 4 67. F = (2y + sin x)i + (z² + (1/3)cos y)j + x*k; r(t) = (sin t)i + (cos t)j + (sin 2t)k, -7/2 < i </2 68. F = (x²y)i + rj + xyk; r(f) = (cos t)i + (sin t)j + (2 sin² t – 1)k, 0<t< 2m
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